Elliptic curve isogeny class 361.1-a over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-361.1-a
• Conductor: 361.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{10}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 10 \); class number \(2\).

Elliptic curves in class 361.1-a over \(\Q(\sqrt{10}) \)

Isogeny class 361.1-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
361.1-a1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -3077\) , \( -64681\bigr] \)
361.1-a2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -37\) , \( -81\bigr] \)
361.1-a3	\( \bigl[0\) , \( -1\) , \( 0\) , \( 3\) , \( -1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph